Matrix equivalence classes with applications

Equivalence Classes of Direction Objects and Applications

Direction is an important spatial relationship that is used in many elds such as geographic information systems(GIS) and image interpretation. It is also frequently used as a selection condition in spatial queries. In our recent work we have described a novel viewpoint to model direction as a `spatial object' based upon the concepts of vectors, points and angles. This was a departure from the c...

Some equivalence classes of operators on B(H)

The graph of equivalence classes and Isoclinism of groups

‎Let $G$ be a non-abelian group and let $Gamma(G)$ be the non-commuting graph of $G$‎. ‎In this paper we define an equivalence relation $sim$ on the set of $V(Gamma(G))=Gsetminus Z(G)$ by taking $xsim y$ if and only if $N(x)=N(y)$‎, ‎where $ N(x)={uin G | x textrm{ and } u textrm{ are adjacent in }Gamma(G)}$ is the open neighborhood of $x$ in $Gamma(G)$‎. ‎We introduce a new graph determined ...

Fuzzy equivalence relations and their equivalence classes

In this paper we investigate various properties of equivalence classes of fuzzy equivalence relations over a complete residuated lattice. We give certain characterizations of fuzzy semipartitions and fuzzy partitions over a complete residuated lattice, as well as over a linearly ordered complete Heyting algebra. In the latter case, for a fuzzy equivalence relation over a linearly ordered comple...

Veriication by State Spaces with Equivalence Classes

This paper demonstrates the potential of veriication based on state spaces reduced by equivalence relations. The basic observation is that quite often, some states of a system are similar, i.e., they induce similar behaviours. Similarity can be formally expressed by deen-ing equivalence relations on the set of states and the set of actions of a system under consideration. A state space can be c...